Epistemic Question
George Dance
A is false." That sounds like a valid theorem of epistemic logic; but
is it? The one book I've read mentioning epistemic logic does not
mention it.
Elaine Jackson
falsified but not verified. Is this relevant?
George Dance <georg...@hotmail.com> wrote in message
news:6312c50b.02010...@posting.google.com...
Daryl McCullough
georg...@hotmail.com says...
It's not true. Statements about the world can have different
logical complexities, and what can be known about their truth
values depends on the complexity.
Here's the start of a classification of types of sentences:
(Roughly following Karl Popper)
1. Observational sentences. These are simple statements of
fact, such as "It is raining". Such a statement can be
checked for its truth---if it is true, you can find out
that it is true, and if it is false, you can find out that
it is false.
2. Verifiable sentences. These are statements that can
be proved true by a single observation, but cannot be
proved false by a single observation.
For example: "It sometimes rains on Valentine's Day". It only
takes a single observation to prove such a statement true, but
it would take an infinite number of observations to
prove it false. A verifiable sentence can be roughly
thought of as the logical "or" of an infinite number of
observational sentences: "It will rain this Valentine's
Day, or it will rain the next Valentine's Day, or it
will rain the Valentine's Day after that or ..."
3. Falsifiable sentences. These are statements that have
the form of a general rule, or a "law". They can be proved
false by a single observation, but cannot be proved true
by a single observation.
For example: "It always rains
on Valentine's Day". You can never know whether such a
sentence is true (it might have been true for every
Valentine's Day in the past, but there is no way of
knowing if it will be true for every Valentine's
Day in the future). A falsifiable sentence can be
roughly thought of as the logical "and" of an infinite
number of observational sentences: "It will rain this
Valentine's Day, and it will rain the next Valentine's
Day, and it will rain the Valentine's Day after that, and ..."
There is no end to the logical complexity of statements. Something
more complex than a falsifiable sentence would be something like
"Every person has an exact double somewhere in the universe". This
is like the logical "and" of an infinite number of verifiable
sentences "Joe has an exact double, and Mary has an exact double,
and Ann has an exact double, ..." (You can prove that somebody
has an exact double, but you cannot prove that they *don't*.)
Another sentence more complex than a falsifiable sentence is
"Somewhere, there is a person who knows everything". This is
like the logical "or" of an infinite number of falsifiable
sentences: "Joe knows everything, or Mary knows everything,
or Ann knows everything, or ..." (You can prove that somebody
doesn't know everything, but you cannot prove that they *do*.)
In summary:
Observational sentence: You can know it is true, and
you can know it is false.
Verifiable sentence: You can know it is true, but you
can never know it is false.
Falsifiable sentence: You can know it is false, but you
can never know it is true.
More complex sentences: You may never know if it is true
and you may never know if it is false.
--
Daryl McCullough
CoGenTex, Inc.
Ithaca, NY
Cant Ng
What if A is necessarily true? Assuming that
1. there are necessary truths that we can know
2. for any X if we know it then it's true
suppose it is possible to know that A is true, and that A is
necessarily true. But if we know A is false, then we know -A, and
then -A is true. However, -A is impossible. So isn't our knowing A
to be false impossible?
Of course, the hole in that argument is, we might somehow have
-A & []A,
but then please tell me what that would mean. Having
[]A => A
would rule it out.
It's possible that Heidi Fleiss knows 694 x 3 = 2082, and it's
impossible that she knows 694 x 3 = 2085. She might wrongly believe
the latter proposition, but (by 2.) she wouldn't know it.
Well, maybe you had in mind empirical props anyway. Anyhow, what kind
of axioms would you like to have?
Max
George Dance
> What about Karl Popper's insistence that scientific theories can be
> falsified but not verified. Is this relevant?
Highly relevant. It tells me that, first, I was generalizing from too
narrow an example of propositions; second, that as whether the
statement below is true depends on the type of proposition A is,
propositional calculus is the wrong logic in which to think about it.
So I'll have to rewrite in fol and restate. Thanks for your feedback.
Bill Taylor
|> Here's the start of a classification of types of sentences:
|>
|> 1. Observational sentences. These are simple statements of
|> fact, such as "It is raining". Such a statement can be
|> checked for its truth---if it is true, you can find out
|> that it is true, and if it is false, you can find out that
|> it is false.
i.e. Quantifier-free statements.
|> 2. Verifiable sentences. These are statements that can
|> be proved true by a single observation, but cannot be
|> proved false by a single observation.
i.e. Existential statements. One quantifier (existential).
|> 3. Falsifiable sentences. These are statements that have
|> the form of a general rule, or a "law". They can be proved
|> false by a single observation, but cannot be proved true
|> by a single observation.
i.e. Universal stements. One quantifier (universal).
|> There is no end to the logical complexity of statements.
Indeed; clearly a hierarchy. But there is some point to grouping all
the remainder together, as "mixed-quantifier" statements. These all
have the common property that they can be neither falsified nor verified
by a finite number of observations. So they require proof (if mathematical),
or substantial agreement (and no disagreement) with the others, if scientific
or everyday statements.
But adopting a very tough logical positivist attitude, these latter statements
are all (strictly) meaningless. I doubt anyone nowadays is so strict.
In any event, there is now a clear-cut bi-dichotomy here, which many people
will recall is one of my favourite sort of things...
verifiable not so
,-----------------------------.
| | | As always, it is to be
falsifiable | facts | universals | conventially understood
| | | that "verifiable" means
|--------------+--------------| "verifiable if true" and
| | | similarly for "falsifiable".
not so | existentials | mixed |
| | |
`-----------------------------'
Or, in everyday applications, as I often like to dub them...
verifiable not so
,-----------------------------.
| | |
falsifiable | facts | scientific |
| | |
|--------------+--------------|
| | |
not so | religious | meaningless |
| | |
`-----------------------------'
Note again that scientific statements and religious ones are again highlighted
as being of essentially opposite types; but that, as a relief to religiosos,
religious staements are still ascribed *some* meaning... it's just that
they almost all happen to be false, in fact.
------------------------------------------------------------------------------
Bill Taylor W.Ta...@math.canterbury.ac.nz
------------------------------------------------------------------------------
One schoolgirl was amused that so many Hispanics
called their children Jesus. That was Christine.
------------------------------------------------------------------------------
Daryl McCullough
>Or, in everyday applications, as I often like to dub them...
>
> verifiable not so
> ,-----------------------------.
> | | |
>falsifiable | facts | scientific |
> | | |
> |--------------+--------------|
> | | |
> not so | religious | meaningless |
> | | |
> `-----------------------------'
>
>Note again that scientific statements and religious ones are again
>highlighted as being of essentially opposite types; but that, as a
>relief to religiosos, religious staements are still ascribed *some*
>meaning... it's just that they almost all happen to be false, in
>fact.
I wouldn't say that religious beliefs are verifiable. Verifiable
means that if correct, it can be proved correct. But consider
something like belief in God. Even if God exists, how would
one prove that he exists? The statement "There exists a guy
who can raise the dead" is possibly verifiable, but verifying
it wouldn't prove that the guy is God, or that he get's his
power from God.
I understand what you're driving at though. Religious people
take various good events as evidence of God
(e.g. somebody makes a miraculous recovery from cancer, somebody
finds a bagel in the shape of Mother Teresa). But they never
consider bad events as evidence of the nonexistence of God
(e.g. when good people die in horrible ways). But I'm not sure
that this is because of the logical nature of religious statements.
Instead, I think it is just that the people who think such things
have a naive view of what constitutes evidence.
Greg Lee
>>Or, in everyday applications, as I often like to dub them...
>>
>> verifiable not so
>> ,-----------------------------.
>> | | |
>>falsifiable | facts | scientific |
>> | | |
>> |--------------+--------------|
>> | | |
>> not so | religious | meaningless |
>> | | |
>> `-----------------------------'
>>
>>Note again that scientific statements and religious ones are again
>>highlighted as being of essentially opposite types; but that, as a
>>relief to religiosos, religious staements are still ascribed *some*
>>meaning... it's just that they almost all happen to be false, in
>>fact.
> I wouldn't say that religious beliefs are verifiable. Verifiable
> means that if correct, it can be proved correct. But consider
> something like belief in God. Even if God exists, how would
> one prove that he exists? The statement "There exists a guy
> who can raise the dead" is possibly verifiable, but verifying
> it wouldn't prove that the guy is God, or that he get's his
> power from God.
Perhaps atheism is a better example. Neither the discovery of
a raiser of the dead, nor any fact I can imagine, would convince
me that God exists. But maybe "(x)~" statements go in a different
box?
That is a really neat diagram.
> I understand what you're driving at though. Religious people
> take various good events as evidence of God
> (e.g. somebody makes a miraculous recovery from cancer, somebody
> finds a bagel in the shape of Mother Teresa). But they never
> consider bad events as evidence of the nonexistence of God
> (e.g. when good people die in horrible ways). But I'm not sure
> that this is because of the logical nature of religious statements.
> Instead, I think it is just that the people who think such things
> have a naive view of what constitutes evidence.
> --
> Daryl McCullough
> CoGenTex, Inc.
> Ithaca, NY
--
Greg Lee <gr...@ling.lll.hawaii.edu>
Jesse F. Hughes
> Daryl McCullough <da...@cogentex.com> wrote:
> > mat...@math.canterbury.ac.nz (Bill Taylor) says...
>
> >>Or, in everyday applications, as I often like to dub them...
> >>
> >> verifiable not so
> >> ,-----------------------------.
> >> | | |
> >>falsifiable | facts | scientific |
> >> | | |
> >> |--------------+--------------|
> >> | | |
> >> not so | religious | meaningless |
> >> | | |
> >> `-----------------------------'
[Big snip -- including all of Daryl's words]
>
> That is a really neat diagram.
Am I the only one to think that this box is naive and overly
ambitious?
Verifiable and non-refutable claims are "religious"? So
the claim that particle X can be split into subparticles is a
religious claim.
Falsifiable and verifiable claims are called "facts"? I would reserve
the word facts for those claims that are not merely verifiable, but
are verified (regardless of refutability).
Refutable and non-verifiable claims are "scientific", while verifiable
and non-refutable claims are "religious". Hence, take any scientific
claim and negate it and you get a religious claim, and vice versa.
Those claims that are neither verifiable nor refutable are meaningless
-- well, here, I suppose my objection depends on what one means by
verifiable and refutable. I'll skip this criticism presently.
Perhaps Bill didn't intend these labels to be taken so seriously, but
merely useful mnemonics. If so, I have no complaint, of course.
--
"The extra care that's needed for such expressions has been turned into
a statement that they can't be used at all in factorizations because
the position is that I haven't proven that once I am no longer using
polynomials that factorizations are still non unique." J. S. Harris
Jesse F. Hughes
>
> Perhaps Bill didn't intend these labels to be taken so seriously, but
> merely useful mnemonics. If so, I have no complaint, of course.
Sorry to follow my own self up, but after posting, I looked up Bill's
original post for context. Must do this before posting once in a
while! I think that Bill took these labels as mnemonics, in which
case my complaints are a bit off the mark.
So, for content: Bill's "meaningless/mixed quantifiers" box could be
expanded. If one looks at formulas of the form (E x)(A y)P(x,y), say
(P quantifier free), then one could view these as "verifiable in the
limit" in the following sense. Imagine that at each second, a person
says "yes" or "no" to the proposition he's testing (we also imagine
new data coming in at each second). We say that a proposition is
verifiable in the limit if it is the case that there is an algorithm
for these judgments such that, if the proposition is true, the person
will reach some time n such that thereafter he always says "yes" and
else he says "no" an infinite number of times. In other words, it's
verifiable in the limit if there is an algorithm such that the
sequences "stabilizes" to yes iff the proposition is true.
(A proposition is verifiable in the simple sense just in case the
person also knows when the sequence has stabilized.)
The algorithm for propositions as above is thus: Pick an x to wager on
and say "yes" until we see a y such that ~P(x,y). If we see such a y,
say "no" and pick a new x to wager on and start over. (More
precisely, one may take x to be 0 to start, and go to the successor
whenever a counterexample is found.)
The careful reader will note the implicit assumption: We must assume
that if the claim is false, then for each x there is some y such that
~P(x,y) will be in our evidence.
Please forgive the somewhat garbled explanation here. I know I've
been imprecise, but I hope this gets the point across that one can
analyze the so-called "meaningless" box further. See Kelly's /The
Logic of Reliable Inquiry/ for details.
--
Jesse Hughes
"[I]f gravel cannot make itself into an animal in a year, how could it
do it in a million years? The animal would be dead before it got
alive." --The Creation Evolution Encyclopedia
Bill Taylor
|> > I wouldn't say that religious beliefs are verifiable.
I would. That also applies to other areas where folk often say
of a fervent follower that "he's almost religious about it".
The key is belief in something more or less existential, whose existence
could *conceivably* be proved, but whose non-existence never could.
(Note the connection here with the perennial "proving a negative" debate.)
Scientific, or more generally, skeptical, statements, are of converse type.
They are *falsifiable* - they take risks; so as well as being more
meaningful they are also more manfully courageous.
For a "typical" religious case, I agree that raising the dead is no example;
indeed that may be quite possible (to a degree) within a century!
A more incontrovertable case would be as follows:-
If fiery chariots were suddenly to rain down from the sky, full of
glowing figures of angels and other demi-gods, and they did marvellous
miracles for weeks and weeks, and generally behaved as religious folk
think they ought to; and all this was witnessed by most of the earth's
population, including all of us on this ng, and was on the news for weeks,
with all sorts of convincing evidence, and the god-figure explained that
the rest of the universe was now being folded up, because he'd finished
his experiment, and that the earth would continue now under the good
new administration...
...well, I'd call that a pretty convincing proof of the "existence of a god"!
And it is *conceivable*... barely... it is not logically impossible.
So yes, that religious statement is *verifiable*, by such a train of events,
but (as we all know) never *falsifiable* (unless the proponents are definite
enough about the god's properties to catch them in a logical contradiction
that they can't wurgle out of).
Incidentally, if a god, anything at all like most of the traditional ones,
*did* exist, I can't for the life of me see why he *doesn't* do all this!
He must be a real sadist to let us go on suffering cancer and kidney stones
indefinitely... so maybe he is just an insect-poking sadist?
Of course, no-one hardly thinks the above verification is ever going to
actually occur, not even the most fervent fundie, but it's *conceivable*.
So Daryl, would you agree to that form of religious verificationism?
|> >>
|> >> verifiable not so
|> >> ,-----------------------------.
|> >> | | |
|> >>falsifiable | facts | scientific |
|> >> | | |
|> >> |--------------+--------------|
|> >> | | |
|> >> not so | religious | meaningless |
|> >> | | |
|> >> `-----------------------------'
|> That is a really neat diagram.
Thank-you Greg, I was rather pleased with it too!
Bi-dichotonies are wonderful things!
Here's another one for you...
a priori a posteriori
.--------------------------.
| | |
synthetic | math | science |
| | |
|------------+-------------| The Kant/Taylor bidichotomy.
| | |
analytic | logic | sophistry! |
| | |
`--------------------------'
------------------------------------------------------------------------------
Bill Taylor W.Ta...@math.canterbury.ac.nz
------------------------------------------------------------------------------
A Creationist is just a flat-earther without the courage of his convictions.
------------------------------------------------------------------------------
George Greene
: |> Daryl McCullough <da...@cogentex.com> wrote:
: |> > I wouldn't say that religious beliefs are verifiable.
Is that properly quoted??
Daryl WOULD SO TOO say that religious beliefs are verifiable.
It is easy to define verification conditions for all of them.
If you are having the appropriate confirmational experience
then that is a verification.
: The key is belief in something more or less existential, whose existence
: could *conceivably* be proved, but whose non-existence never could.
: (Note the connection here with the perennial "proving a negative" debate.)
Bill is right.
: Scientific, or more generally, skeptical, statements, are of converse type.
: They are *falsifiable* -
Again, in, and only in, PRINCIPLE.
If your scientific theory is even halfway correct then
a significant subset of its statements are in fact NOT
falsifiable, pragmatically. But they still are theoretically;
there is (in theory, conceivably, definably) a *semantically*
possible (even if it is not physically possible) observational
outcome that could falsify them.
: For a "typical" religious case, I agree that raising the dead is no example;
: indeed that may be quite possible (to a degree) within a century!
: A more incontrovertable case would be as follows:-
:
: If fiery chariots were suddenly to rain down from the sky, full of
: glowing figures of angels and other demi-gods, and they did marvellous
: miracles for weeks and weeks, and generally behaved as religious folk
: think they ought to;
No, please, nothing along this tack is even remotely in the ballpark.
It is always possible that the factual actual physical cause of this
is something other than what you think it is. The relevant experience
is mental, is internal, involves some interaction between whatever your
religious belief is a belief IN and your SOUL. And when this interaction
is factually occurring, your soul does/will in fact accurately perceive
(in a very confirmed and fulfilled way) THAT it is in fact occurring.
But "it" here can NEVER be any MERELY physically observable thing,
NOT EVEN fiery chariots raining down from the sky doing marvelous
(physically-defined) miracles, and "generally behaving as religious
folk think they ought to" is just SPECTACULARLY irrelevant.
Religious folk generally are factually deluded, ESPECIALLY about their
own religions.
: and all this was witnessed by most of the earth's
: population, including all of us on this ng, and was on the news for weeks,
: with all sorts of convincing evidence,
There is no such thing as convincing evidence, in the physical
realm, of anything in the spiritual realm. The closest you could
get would be physical occurrences that violated heretofore unviolated
laws of physics, and even then, the explanation for the change
could be something other than any particular religion's preferred
one, whence the miracles would NOT constitute "verification" of
the religion's tenets.
: and the god-figure explained that
: the rest of the universe was now being folded up, because he'd finished
: his experiment, and that the earth would continue now under the good
: new administration...
Well, He could JUST BE *LYING*, and his doing that might not
verify much of ANY religious beliefs.
: So yes, that religious statement is *verifiable*, by such a train of events,
Well, I disagree, but the point is, there are religious statements that
are verifiable by chains of events, even if they cannot be external to
the mind in which the verification is occurring.
: Bi-dichotonies are wonderful things!
Yeah, I agree in principle that the one above
should just be taken as definitional. The objections
are willful obscurantism masquerading as deliberate density.
: Here's another one for you...
:
: a priori a posteriori
: .--------------------------.
: | | |
: synthetic | math | science |
: | | |
: |------------+-------------| The Kant/Taylor bidichotomy.
: | | |
: analytic | logic | sophistry! |
: | | |
: `--------------------------'
I don't like this one, though. Synthetic a priori
just plain doesn't exist. Math is a subset of logic.
Math is purely about what follows logically, i.e.
analytically, from the axiom-set defining the particular
subfield of math. That's one of the reasons why
the British talk about "maths" instead of math.
---
"It's difficult ... you need to be united to have any
strength, but internal issues have to be addressed."
--- E. Ray Lewis, on liberalism in America
Daryl McCullough
>If fiery chariots were suddenly to rain down from the sky, full of
>glowing figures of angels and other demi-gods, and they did marvellous
>miracles for weeks and weeks, and generally behaved as religious folk
>think they ought to; and all this was witnessed by most of the earth's
>population, including all of us on this ng, and was on the news for weeks,
>with all sorts of convincing evidence, and the god-figure explained that
>the rest of the universe was now being folded up, because he'd finished
>his experiment, and that the earth would continue now under the good
>new administration...
>
>...well, I'd call that a pretty convincing proof of the "existence of a
>god"!
I wouldn't. I would call it pretty convincing proof of the
existence of someone with godlike powers. But it doesn't
follow that this person is omnipotent, or omniscient, or
that he/she created the Earth, or that this person merits
worship.
>So yes, that religious statement is *verifiable*,
I disagree. That is verification only in the weak sense
that everything seen is *consistent* with the theory that
the person is a god, and it is difficult to come up with
a plausible alternative explanation. But that's true of
scientific theories, as well. Lasers (or superfluids)
are predicted by Bose-Einstein statistics, and it is
difficult to come up with an alternative explanation
for how lasers (or superfluids) work.
For practical purposes, the existence of lasers
and superfluids verify Bose-Einstein statistics.
But logically speaking, those phenomena are only consistent
with the theory, they don't imply the theory.
>by such a train of events, but (as we all know) never
>*falsifiable* (unless the proponents are definite
>enough about the god's properties to catch them in
>a logical contradiction that they can't wurgle out of).
Many religious beliefs *are* falsifiable in that sense.
If you believe that anyone who does such and such evil
act will be struck down by lightning, that is falsifiable.
If you believe that the second coming of Christ will happen
in the year 2000, that belief is falsifiable.
Of course, I think that modern religious people tend to
shy away from making *either* verifiable or falsifiable
claims. Religion colors their interpretation of what
happens in the world, but it doesn't make any predictions.
>Incidentally, if a god, anything at all like most of the
>traditional ones, *did* exist, I can't for the life of me
>see why he *doesn't* do all this! He must be a real sadist
>to let us go on suffering cancer and kidney stones
>indefinitely... so maybe he is just an insect-poking sadist?
I disagree. A universe in which God pokes his nose in
everything, fixing our boo-boos and making sure nothing
bad ever happens doesn't sound like a good universe to me.
It sounds completely boring. As I said once before, I think
that if he existed, God's relationship to the world would be
like the relationship between an author and his novel. An
author may love his characters, in a sense, but he won't
protect them from all harm, because that would make the
story boring and pointless.
Daryl McCullough
>
>mat...@math.canterbury.ac.nz (Bill Taylor) writes:
> : If fiery chariots were suddenly to rain down from the sky, full of
> : glowing figures of angels and other demi-gods, and they did marvellous
> : miracles for weeks and weeks, and generally behaved as religious folk
> : think they ought to;
>
>No, please, nothing along this tack is even remotely in the ballpark.
>It is always possible that the factual actual physical cause of this
>is something other than what you think it is. The relevant experience
>is mental, is internal, involves some interaction between whatever your
>religious belief is a belief IN and your SOUL. And when this interaction
>is factually occurring, your soul does/will in fact accurately perceive
>(in a very confirmed and fulfilled way) THAT it is in fact occurring.
>But "it" here can NEVER be any MERELY physically observable thing,
>NOT EVEN fiery chariots raining down from the sky doing marvelous
>(physically-defined) miracles, and "generally behaving as religious
>folk think they ought to" is just SPECTACULARLY irrelevant.
>Religious folk generally are factually deluded, ESPECIALLY about their
>own religions.
Okay, I can agree with this form of internal verificationism for
religious beliefs. I was thinking along the lines Bill
was saying---about *public* events verifying religious truths.
I don't think that that can ever happen. There will always be
a nonreligious explanation for any purely physical phenomenon.
George Dance
> georg...@hotmail.com (George Dance) wrote in message news:<6312c50b.02010...@posting.google.com>...]
> > "If it is possible to know that A is true, it is possible to know that
> > A is false." That sounds like a valid theorem of epistemic logic; but
> > is it? The one book I've read mentioning epistemic logic does not
> > mention it.
>
> What if A is necessarily true? Assuming that
>
> 1. there are necessary truths that we can know
> 2. for any X if we know it then it's true
>
> suppose it is possible to know that A is true, and that A is
> necessarily true. But if we know A is false, then we know -A, and
> then -A is true. However, -A is impossible. So isn't our knowing A
> to be false impossible?
Sounds true. One can only know something is false, if it is false; or
true, if it is true.
snip
> Well, maybe you had in mind empirical props anyway. Anyhow, what kind
> of axioms would you like to have?
>
> Max
After reading the comments on this for a week (and they've been good
comments), I think the possible axioms that best capture what I
originally was thinking of (as vs. what I actually said), are:
1. (((3x)Fx)->(<>K(3x)Fx))<->(((3x)~Fx)->(<>K(3x)~Fx))
2. (<>(3x)Fx&<>(3x)~Fx)->(<>K(3x)Fx<-><>K(3x)~Fx)
(3x)=df."There is at least one x." <>=df."It is possible that..."
K=df."It is known that..."
1. seems to best capture my original claim. 1. is not a theorem, of
course; which is why it would have to be added as an axiom.
I would appreciate your further comments.
George Greene
: Many religious beliefs *are* falsifiable in that sense.
: If you believe that anyone who does such and such evil
: act will be struck down by lightning, that is falsifiable.
Not in the short run. It matters whether your belief
does or doesn't specify HOW LONG we'll have to wait for
the strike-down to get around to happening.
: If you believe that the second coming of Christ will happen
: in the year 2000, that belief is falsifiable.
Not before 2000 it isn't. And this matters a lot.
Spacetime as we currently scientifically conceive it
is isotropic. Most physics experiments worthy of the name
have the property that it DOES NOT MATTER when in time, or
where in space, OR BY WHOM, they get conducted&observed.
It may matter what the local gravitational or electromagnetic
fields are doing, or how fast the observer is moving,
but assuming the experiment specifies how you have to set
those, then it MATTERS that the experimental outcome will
be the SAME regardLESS of time or place. And this matters
even more because you can't actually even STATE a time or
place in most scientific theories: the best you can have
is A FRAME OF REFERENCE. All your co-ordinates for times
and places are stated in terms OF THAT FRAME, and how that
frame relates to ACTUAL times and places must in fact
be specified INformally, METAtheoretically, OUTSIDE the
scientific theory that the experiment is possibly falsifying.
So anything that has "2000" in it AT ALL arguably isn't
even on the radar screen, not without a clear translation
of "2000" into some more physically definable units.
My point being simply that "2000" cannot mean 2000 years
after the birth of Christ since nobody knows exactly
when Christ was born but we do know it was closer to 4 B.C.
than 1 A.D., and we do know some historians made calendar
errors since.
That science is INDEPENDENT of place, time, and person/observer
is sort of a metaphysical axiom that is missing in action
here. "I am here now" is either not scientific at all
or trivially axiomatic/tautologous in the speaker's frame
of reference.
Bill Taylor
|> >...well, I'd call that a pretty convincing proof of the "existence of a god"!
|>
|> I wouldn't. I would call it pretty convincing proof of the
|> existence of someone with godlike powers.
Well - I *did* include the folding up of and putting away of the rest of the
universe, and miracles, so those godlike powers are pretty much omnipotence.
If it walks like a duck and quacks like a duck...
I feel you're quibbling.
|> > so maybe he is just an insect-poking sadist?
|> I disagree. A universe in which God pokes his nose in
|> everything, fixing our boo-boos and making sure nothing
|> bad ever happens doesn't sound like a good universe to me.
I disagree. It sounds wonderful to me. Indeed, it sounds like heaven! :-)
Saying "poking his nose in" is prejudicial lingo... a proper loving god
*ought* to poke his nose in to execute justice and make sure no-one has
to suffer from the free-will of others. One can still allow free will
without letting nasties run rampant.
And as for cancer... well... god is clearly breaking his own rules.
Loving *and* omnipotent... give us a break puh-leeeez!
|> It sounds completely boring.
What nonsense. There can still be music, math, games, love, all that stuff...
not boring at all! To say boring just because there's no suffering shows
an astonishing lack of imagination.
|> like the relationship between an author and his novel. An
|> author may love his characters, in a sense, but he won't
|> protect them from all harm, because that would make the
|> story boring and pointless.
The key difference is, the characters in a book don't feel *real* agony.
What we actually have is not characters in a book, but animals in
a menagerie who are being poked, prodded and tortured by the owner
for the sake of seeing what happens... oh, and "for their own interest".
As a religious apologist you're fasiling miserably here, Daryl.
Don't give up your philosophical day job...
------------------------------------------------------------------------------
Bill Taylor W.Ta...@math.canterbury.ac.nz
------------------------------------------------------------------------------
Urgently needed: An antidote for the cancerous meme of religious belief.
------------------------------------------------------------------------------
Cant Ng
>I think the possible axioms that best capture what I
> originally was thinking of (as vs. what I actually said), are:
>
> 1. (((3x)Fx)->(<>K(3x)Fx))<->(((3x)~Fx)->(<>K(3x)~Fx))
>
> 2. (<>(3x)Fx&<>(3x)~Fx)->(<>K(3x)Fx<-><>K(3x)~Fx)
>
> (3x)=df."There is at least one x." <>=df."It is possible that..."
> K=df."It is known that..."
I'm trying to wrap my brain around those, but am stuck a little on the
basics. How do "K" and "<>" behave together? There's an ambiguity
when we say "possibly it's known that p." (Temporarily eschewing
quantifiers.)
For we might like either
a. <>K(p) -> <>p
or
b. <>K(p) -> p.
In most of the (admittedly few) accessible worlds where the Red Wings
did not come back and beat the Canucks in OT, it is known that they
didn't. That's the a.-sense for <>K , that if some decidable p is
possibly true, then possibly it's known to be true. K(p) is true in a
subset of the possible worlds in which p is true.
On the other hand, b. doesn't agree with that interpretation, because
if p is false at w, then contrapositively ~<>K(p).
How about [](K(p) -> p) ?
Are you interested in the modality of the "existence" of knowledge
about matters of fact? E.g., how we can say, "I might have known
(even if I were no better at coming to know than I am now)." Also we
can consider how our ways of coming-to-know could differ (e.g.,
they're different from how they used to be, and they'll change).
Since the possibility of falsification/verification is sometimes
considered to be a condition of the meaningfulness of a proposition,
change in our ability to make observations (or inferences from the
obs.) gets associated with revision of the class of propositions that
are meaningful. Then we would want to avoid the tricky position of,
e.g., trying to identify what proposition is being verified at a
possible world, while being unable to recognize or comprehend the
means of verification. On the other hand I don't want to overstate
the significance of this incommensurability scenario, because there is
a wide margin between practical verifiability and nonsense, i.e.,
being able to spell out the physically possible means of verification.
In any case, difference in our ways of coming-to-know entails a whole
lot of differences of fact.
Max
George Dance
> georg...@hotmail.com (George Dance) wrote in message news:<6312c50b.02011...@posting.google.com>...
>
> >I think the possible axioms that best capture what I
> > originally was thinking of (as vs. what I actually said), are:
> >
> > 1. (((3x)Fx)->(<>K(3x)Fx))<->(((3x)~Fx)->(<>K(3x)~Fx))
> >
> > 2. (<>(3x)Fx&<>(3x)~Fx)->(<>K(3x)Fx<-><>K(3x)~Fx)
> >
> > (3x)=df."There is at least one x." <>=df."It is possible that..."
> > K=df."It is known that..."
>
> I'm trying to wrap my brain around those, but am stuck a little on the
> basics.
You are doing a very good job of getting me to see the basics here,
myself.
> How do "K" and "<>" behave together? There's an ambiguity
> when we say "possibly it's known that p." (Temporarily eschewing
> quantifiers.)
>
> For we might like either
>
> a. <>K(p) -> <>p
>
> or
>
> b. <>K(p) -> p.
>
> In most of the (admittedly few) accessible worlds where the Red Wings
> did not come back and beat the Canucks in OT, it is known that they
> didn't. That's the a.-sense for <>K , that if some decidable p is
> possibly true, then possibly it's known to be true. K(p) is true in a
> subset of the possible worlds in which p is true.
That's the sense of <>K that I want; strict logical possibility. I
can only know tonight that the sun has gone down, for instance, only
if it were possible for me to know that the sun had not gone down (if
that had happened instead).
> On the other hand, b. doesn't agree with that interpretation, because
> if p is false at w, then contrapositively ~<>K(p).
Right; ~p->[]~K(p) is strictly implied by b.
>
> How about [](K(p) -> p)?
Well, that's a good place to start, as it's axiomatically true. So
Iet's let's see where it leads:
1. [](K(p) ->p)
Axiom T
2. [](~p->~K(p)) 1
contra
3. [](~p->~K(p)) -> ([]~p->[]~K(p)) 2 Axiom K
4. []~p->[]~K(p) 2,3 MP
5. ~<>p->~<>K(p) 4 MN
6. <>K(p)-><>p 5 contra
So
> a. <>K(p) -> <>p
turns out to be a valid theorem, while
> b. <>K(p) -> p.
looks like an example of committing the fallacy of
misconditionalization on step 2 of the argument.
> Are you interested in the modality of the "existence" of knowledge
> about matters of fact? E.g., how we can say, "I might have known
> (even if I were no better at coming to know than I am now)." Also we
> can consider how our ways of coming-to-know could differ (e.g.,
> they're different from how they used to be, and they'll change).
I think that should be included in a system of epistemic logic; but
I'm a long way from knowing how to. I've heard of non-epistemic
systems that have a second modal operator for 'contingent necessity'
(to model physical causation, eg), and I guess that would be the best
way to model the practical limitations you're talking of.
> Since the possibility of falsification/verification is sometimes
> considered to be a condition of the meaningfulness of a proposition,
> change in our ability to make observations (or inferences from the
> obs.) gets associated with revision of the class of propositions that
> are meaningful. Then we would want to avoid the tricky position of,
> e.g., trying to identify what proposition is being verified at a
> possible world, while being unable to recognize or comprehend the
> means of verification. On the other hand I don't want to overstate
> the significance of this incommensurability scenario, because there is
> a wide margin between practical verifiability and nonsense, i.e.,
> being able to spell out the physically possible means of verification.
> In any case, difference in our ways of coming-to-know entails a whole
> lot of differences of fact.
I think it's best for this particular matter to avoid the question of
meaninglessness simply by restricting the domain to propositions that
either are true or are false, and in either case meaningful; otherwise
we don't even have pv~p and ~(p&~p) to begin with.
Daryl McCullough
>
>da...@cogentex.com (Daryl McCullough) writes:
>
>|> >...well, I'd call that a pretty convincing proof of the "existence of a
>god"!
>|>
>|> I wouldn't. I would call it pretty convincing proof of the
>|> existence of someone with godlike powers.
>
>Well - I *did* include the folding up of and putting away of the rest of the
>universe, and miracles, so those godlike powers are pretty much omnipotence.
>If it walks like a duck and quacks like a duck...
>
>I feel you're quibbling.
It's exactly the sort of quibble as when someone says
that quantum mechanics, or relativity has not been proved
correct. In other words, it's not a quibble, it's exactly
the sort of distinction (between falsifiable and verifiable)
that we are discussing.
>|> > so maybe he is just an insect-poking sadist?
>|> I disagree. A universe in which God pokes his nose in
>|> everything, fixing our boo-boos and making sure nothing
>|> bad ever happens doesn't sound like a good universe to me.
>
>I disagree. It sounds wonderful to me. Indeed, it sounds like heaven! :-)
Well, we disagree. I happen to believe that what is wonderful
about our world and what is terrible about it are two sides of
the same coin. Entropy.
>Saying "poking his nose in" is prejudicial lingo... a proper loving god
>*ought* to poke his nose in to execute justice and make sure no-one has
>to suffer from the free-will of others.
What makes an atheist an expert on the proper behavior of gods?
>|> It sounds completely boring.
>
>What nonsense. There can still be music, math, games, love,
>all that stuff... not boring at all! To say boring just
>because there's no suffering shows an astonishing lack of
>imagination.
I would pit my imagination against yours any day of the week.
Name a place and a time!
>|> like the relationship between an author and his novel. An
>|> author may love his characters, in a sense, but he won't
>|> protect them from all harm, because that would make the
>|> story boring and pointless.
>
>The key difference is, the characters in a book don't feel *real*
>agony.
How do you know?
>What we actually have is not characters in a book, but animals in
>a menagerie who are being poked, prodded and tortured by the owner
>for the sake of seeing what happens... oh, and "for their own interest".
God is specifically *not* poking us and prodding us! He's *not*
intervening. You're contradicting yourself here, Bill.
>As a religious apologist you're fasiling miserably here, Daryl.
>Don't give up your philosophical day job...
I would say that you are fasiling much worse than I am.
Daryl McCullough
>As a religious apologist you're fasiling miserably here, Daryl.
>Don't give up your philosophical day job...
I'm just pointing out that most of what you say about religion
doesn't make any sense. That's different from saying anything
positive about religion.
Daryl McCullough
>I feel you're quibbling...
>What nonsense...
>...an astonishing lack of imagination.
>...As a religious apologist you're fasiling miserably here, Daryl.
>Don't give up your philosophical day job...
Bill, at some point you claimed (to Keith Ramsay, I believe)
that you are above average when it comes to politeness. But
it does seem that you have trouble disagreeing without being
insulting.
Chris Menzel
> >The key difference is, the characters in a book don't feel *real*
> >agony.
>
> How do you know?
Because someone made them up. They aren't real. They don't really
exist. Things that don't exist don't feel pain.
Not to deny that oceans of ink have been spilled over this issue, but
the controversies consist largely in what these claims *mean*, not
whether they are true. Surely you don't find it reasonable to doubt
them.
Chris Menzel
Daryl McCullough
Before answering, let me back up a little.
In this thread, we were discussing different types of
statements: My classification was (1) observational
(you can look to see if it is true or not) (2) verifiable
(if true, it is possible to discover tell that it is true)
(3) falsifiable (if false, it is possible to discover that
it is false) (4) metaphysical (none of the above).
My claim is that questions about God and reality are
metaphysical, rather than verifiable or falsifiable.
Yes, you can certainly dismiss some views as "unreasonable"
based on how eccentric they sound, but that is a much
less satisfying refutation than the falsification of
a scientific theory. For one thing, it's hard to know
how much of what is considered "reasonable" is a matter
of tradition, rather than actual reason.
I was sketching a possible metaphysics that gives
a role for a God. In such a metaphysics, rather than
being "real" or "unreal" there would be a hierarchy
of "levels of reality". Things that exist only in
the mind of God have a certain level of reality
which is less than that of God, but more than that
of something (like Sherlock Holmes) that exists only
in the minds of people.
Whether this metaphysics is reasonable or not, I
can't say, since I don't really know of a good
criterion for "reasonableness" for metaphysical
questions.
Greg Lee
> On 14 Jan 2002 06:24:53 -0800, Daryl McCullough <da...@cogentex.com> said:
>> >The key difference is, the characters in a book don't feel *real*
>> >agony.
>>
>> How do you know?
> Because someone made them up. They aren't real. They don't really
> exist. Things that don't exist don't feel pain.
And thus the characters in a book really don't feel agony. But the
earlier statement was that they don't feel real agony, which is
a little different. It's rather strange to say Sherlock Holmes
didn't smoke a real pipe, unless of course you think the thing
he smoked wasn't really a pipe. But that doesn't follow from his
failure to exist.
> Not to deny that oceans of ink have been spilled over this issue, but
> the controversies consist largely in what these claims *mean*, not
> whether they are true. Surely you don't find it reasonable to doubt
> them.
So they're surely true, yet of uncertain meaning?
--
Greg Lee <gr...@ling.lll.hawaii.edu>
Bill Taylor
|> >I feel you're quibbling.
|> It's exactly the sort of quibble as when someone says
|> that quantum mechanics, or relativity has not been proved correct.
Ouch. We're getting into naive undergraduate pernickettism here, both if us.
Seems unlikely any further discussion on this will lead to more light than heat!
|> Well, we disagree. I happen to believe that what is wonderful about
|> our world and what is terrible about it are two sides of the same coin.
You begin to sound like a masochist!
> Entropy.
A randomly thermodynamic masochist.
|> What makes an atheist an expert on the proper behavior of gods?
Who better? Never call on a judge to judge his own case.
Anyway, "atheist" is too severe. I prefer skeptic. If you must have
a religious term, call me an unbeliever. Alternatively, call me a cab.
|> I would pit my imagination against yours any day of the week.
It's a match!
|> Name a place and a time!
Your first test of imagination, is to guess when and where it will be!
|> >The key difference is, the characters in a book don't feel *real* agony.
|> How do you know?
I asked them, and that's what they said. I have no reason to doubt them.
|> God is specifically *not* poking us and prodding us!
Oh well not directly, with a giant finger coming down through the clouds, no.
But if all this mess is the handiwork of an omni(pot/sci)ent god, as many say,
he has made a total bollocks of it, and deserves the sack for incompetence.
|> >As a religious apologist you're fasiling miserably here, Daryl.
|> >Don't give up your philosophical day job...
|>
|> I would say that you are fasiling much worse than I am.
I've never fasilled in my life! How dare you sir!!
|> Bill, at some point you claimed (to Keith Ramsay, I believe)
|> that you are above average when it comes to politeness.
Actually I didn't claim that, but near enough. And chiefly for newbies.
|> But it does seem that you have trouble disagreeing without being insulting.
Oh gee whiz Daryl, old son, come down a little. I've praised your efforts
continually; even that very post started off with a compliment! That was
just a bit of comradely banter! I never expected you, of all people, who
knows me well, to take it seriously. Obviously I should sprinkle more
smileys about. Sorry for any momentary offense. Mea culpa.
------------------------------------------------------------------------------
Bill Taylor W.Ta...@math.canterbury.ac.nz
------------------------------------------------------------------------------
What the world needs is not more "think tanks", but more skeptic tanks!
------------------------------------------------------------------------------
Tim Chambers
georg...@hotmail.com (George Dance) wrote:
> can...@canada.com (Cant Ng) wrote in message
> news:<631b4fb0.0201...@posting.google.com>...
> >
> > [1] How about [](K(p) -> p)?
>
> Well, that's a good place to start, as it's axiomatically true. So
> Iet's let's see where it leads:
In this context, you might find (what's called) the
"Paradox of Knowability" intriguing. In particular,
the paradox is set up by taking the above "axiomatically
true" claim -- sometimes called the "factivity condition"
on knowledge -- and coupling it with the claims that
[2] All truths are knowable (in symbols: (Ap)(p -> <>K(p))),
and [3] assorted inferences of first-order, and modal/epistemic,
logic: (a) [](K(p & q) -> Kp & Kq) (intuitively: necessarily,
if you know a conjunction, then you know its conjuncts);
(b) classical first-order logic; (c) etc.
What's striking is that, from the foregoing premises, there's
a prima facie argument that all truths are, *in fact*, known!
(Fitch, in "A Logical Analysis of Some Value Concepts" is credited
with first putting the proof in print; he, in turn, credits an
anonymous referee for pointing it out.) Here goes (the proof is
by reductio):
[4] -(Ap)(p -> Kp).....Assumption for RAA
[5] (3p)(p & -Kp)......by [4] and [3(b)]
[6] (p* & -Kp*)........instantiation of [5]'s existential q'er
[7] [(p* & -Kp*) -> <>K(p* & -Kp*)].....instance of [2]
[8] <>(K(p* & -Kp*))....[6],[7] modus ponens
[9] <>(K(p*) & K-K(p*))[8], and [3a]
[10] <>(K(p*) & -K(p*))...[9] and instance of [1]
[11] Eek!...............[10] proclaims a contradiciton is possible
[12] --(Ap)(p->Kp)......[4]thru[11] RAA
[13] (Ap)(p->Kp)........[12] and [3(b); here, double-negation elim]
But *that* can't be! So, what follows? A few notes on the foregoing
argument are in order...
Note 1: Some -- Dorothy Edgington (in a 1985 issue of the journal,
_Mind_, and Timothy Williamson (in a 1988 issue of the Philosophical
Quarterly) -- argue that we're *already* up a creek at line [8].
Think about it: what would it be *like* to know a claim *and*
know that you don't know it?! Compare "Moore's Paradox" here.
Note 2: The foregoing proof is often deployed against so-called
"anti-realists," for it's argued that they're committed to premise
[2]. In other words, given the absurd upshot of [1], [2] and [3],
and the seeming plausibility of [1] and [3], then the foregoing
paradox shows that [2] is false. In which case, the "anti-anti-
realist" (a.k.a. "realist" ;)) proclaims that the Knowability
Paradox is a reduction of *anti-realism* to absurdity.
*Must* we deny [2]? Some have been less sure -- in particular...:
Note 3: In reply, friends of "anti-realism" have suggested that
it's open to the anti-realist to deny classical first-order logic
in favor of an intuitionist calculus of quantifiers. (In that
case, steps [4] and [12] would no longer logically suffice for
inferring steps [5] and [13], respectively. (Williamson defends
this position; what the Knowability Paradox shows, he argues, is
not that "anti-realism" is spurious -- but, rather, that the
anti-realist ought to opt for intuitionistic logic.)
Note 4: In a 1980 contribution to the journal _Analysis_, J.L.
Mackie made this move: deny [1]! That is, instead of interpreting
"Kp" in a way which entails "p" is true -- as [1] does -- opt for
a "non-factive" gloss (e.g., "There is good evidence for p" or
"p is confirmed").
Williamson et al, by the way, agree with Mackie's claim; but
suggest that this is insufficient for defusing the Knowabiliity
Paradox *unless* the anti-realist also "goes intuitionist".
(The grounds are, roughly, that denying [1] only blocks the step
from [9] to [10] -- but, as we saw at Note 1, we're *already* up
a creek if we get as far as step [8]. So blocking the "factivity
of knowledge," alone, is insufficient for blocking the Knowability
Paradox.)
Anyhow...I just thought you might be interested in a line of
thought which has led some to deny that [1] is "axiomatic."
And, in any case, the Paradox of Knowability is a lot of fun.
Best Wishes,
Tim :)
Sandy Hodges
Tim Chambers wrote:
> [ clip ]
> > > [1] How about [](K(p) -> p)?
[ clip ]
> [2] All truths are knowable (in symbols: (Ap)(p -> <>K(p))),
>
>
[ clip ]
> [4] -(Ap)(p -> Kp).....Assumption for RAA
> [5] (3p)(p & -Kp)......by [4] and [3(b)]
> [6] (p* & -Kp*)........instantiation of [5]'s existential q'er
> [7] [(p* & -Kp*) -> <>K(p* & -Kp*)].....instance of [2]
Most interesting. If x is true, then we might, in some future time,
come to know x. But suppose x is such that the fact that we know x,
changes the truth value of x? That's the case here, if x is (p* &
~Kp*). If we come to know x, we will know p*, which changes the truth
value of ~Kp*, which changes the truth value of x.
So while the Liar results from the fact that our own statements are part
of the world we are describing, this paradox results from us knowing a
world in which our own states of knowledge are part of the world we seek
to know.
Axiom [2] is true from the perspective of an outside observer, who is
not talking about his own states of knowledge, but only about other
peoples'.
If the conclusion is to keep the concept 'Know' but to discard axiom
[2], then that decision is not consistent with discarding 'True' (or
restricting it so that only a meta-language can refer to an object
language), and keeping the rule of the excluded middle.
-- ----- ------ - - --Sandy Hodges / Alameda, California, USA
Mail to Sandy...@attbi.com will reach me.